Biodiesel Produced from Catalyzed Transesterification of Triglycerides Using ion-Exchanged Zeolite Beta and MCM-22

AbstractIn this work, biodiesel production from catalyzed transesterification of triglycerides with excess methanol was studied by using ion-exchanged Zeolite Beta and MCM-22 as heterogeneous catalysts. Zeolite Beta and MCM-22 were synthesized with hydrothermal processes and, subsequently, modified by ion-exchanged with alkali ions. These as-obtained zeolite catalysts could yield a high conversion of triglycerides to biodiesel. The conversion efficiency was largely affected by crystallinity and frameworks of zeolite support, pH value of alkali ion-exchange solutions and alkali loadings onto the zeolite support. Furthermore, the effects of the duration of the sodium ion-exchange process on the final conversion efficiency of triolein to biodiesel, both the as-prepared Zeolite MCM-22 and Zeolite Beta catalysts were used. The effect of the duration of the sodium ion-exchange process is insignificant in transesterification using Na-ion-exchanged Zeolite MCM-22 catalysts from 0.5 to 4h. In contrast, the conversion efficiency of triolein to biodiesel reached ca. 95% in 0.5hours of transesterification using Zeolite Beta ion-exchanged with 3 mmol-eq. Na+/g cat for 0.5hours

Hawking Radiation Under Generalized Uncertainty Principle

The generalized uncertainty relation is expected to be an essential element in a theory of quantum gravity. In this work, we examine its effect on the Hawking radiation of a Schwarzschild black hole formed from collapse by incorporating a minimal uncertainty length scale into the radial coordinate of the background. This is implemented in both the ingoing Vaidya coordinates and a family of freely falling coordinates. We find that, regardless of the choice of the coordinate system, Hawking radiation is turned off at around the scrambling time. Interestingly, this phenomenon occurs while the Hawking temperature remains largely unmodified.Comment: 23 pages, 1 figur

UV Dispersive Effects on Hawking Radiation

We revisit the connection between Hawking radiation and high-frequency dispersions for a Schwarzschild black hole following the work of Brout et al.. After confirming the robustness of Hawking radiation for monotonic dispersion relations, we consider non-monotonic dispersion relations that deviate from the standard relation only in the trans-Planckian domain. Contrary to the common belief that Hawking radiation is insensitive to UV physics, it turns out that Hawking radiation is subject to significant modifications after the scrambling time. Depending on the UV physics at the singularity, the amplitude of Hawking radiation could diminish after the scrambling time, while the Hawking temperature remains the same. Our finding is thus not contradictory to earlier works regarding the robustness of Hawking temperature.Comment: 24 pages, 8 figure